Summary
In my work on Multi Dimensional Forces I defined polygonal wave forms for forces from even numbered dimensions.
I am updating that work to show how the F wave can have phases that effectively swap wavelength for amplitude and vice versa.
This can be applied to waves of any higher dimensions as long as the dimensions the wave exists in are neighbours.
The key to this feature is that the ztar is allowed to rotate with each phase,
Formation of Multi Dimensional Phases
Inter Dimensional Forces
The page on Complex Vectors left us with the question of how could a 3D area translate onto a length in 4D in practical terms?
In figure (Creation of Inter Dimensional Boundary Forces 1) the ztar is used to transmit the force from 3D (for example).
If the wavelengths change by swapping nature so must the heights of any Inter Dimensional Boundary Force so that the work done remains constant.
This can be achieved by rotating the ztar so that the imaginary and real axes change position every 90 degrees or wave phase (see figure Creation
of Inter Dimensional Boundary Forces 2).
Previously I have only consider 4D waves in my Multi Dimensional forces hypothesis as originating form a cube. If we consider a cuboid instead
then the resulting waveform is more like my F wave. Inter Dimensional Forces can therefore exist between any two dimensions that are neighbours.
Exponential Forces
For forces acting onto or from the complex plane and 3D (see figure Creation of Inter Dimensional Boundary Forces 3) a similar method will
explain how waves can transfer between planes. The difficulty is that we do not see any forces acting logarithmically in 3D. They tend to
present themselves as exponential in 3D. So this suggests that the exponential forces in 3D could be reacting to forces on the complex plane.
One explanation for this is that when forces act in the complex plane into 3D, say, the result is Complex Folding. Complex Folding effectively
compresses the logarithic axis onto a linear axis. So this could be interpreted as an exponential effect.
So in the complex plane we have an active wave of exponential length and linear height transforming into a reactive 3D wave of linear
length and exponential height.
